HDMI is a digital signal, whereas the 'component' signal to which you are trying to convert is analogue.  Hence the adaptor that you purchase will have to include a Digital to Analogue converter, rather than just a straightforward lead.  These are available from Amazon and the like.

In picture-quality terms, you may be better off using an hdmi switcher or matrix.

I tried to respond to this earlier but think the post must be in moderation!  Basically, hdmi is digital and component (the input you are trying to use) is analogue, hence you need an adaptor that does the digital to analogue conversion rather than a simple cable adaptor.

It may be easier (and better quality) to use an hdmi switching box or matrix.

Hi Guy,

Thanks for your response. Is this a suitable example of what I need to buy?

No, that one converts in the other direction (component to hdmi).  You want HDMI to component, like this:

To be honest in your shoes I would look at an hdmi switch box - life will be much simpler! 

I am not an expert, but some of these (hdmi matrices) can be controlled by the B&O TV itself using the inbuilt PUC facility - hopefully others can add advice if you want to go this route.